Simeone's charges were beaten by Barcelona on away goals following a 0-0 draw at Camp Nou, with Neymar's headed effort at the Vicente Calderon Stadium in the first leg proving decisive.
However, the former Argentina international believes that Atletico's performance showed signs of promise.
"This trophy does not guarantee anything, but there is a great and growing commitment from this team and that I am very proud of," he said.
"The game was how we imagined it would be, in both legs. They have been playing well for years and we continue to grow, with pride and knowing what we have to do."
Atletico clinched the Copa Del Rey last season after a 2-1 win over city rivals Real Madrid at the Santiago Bernabeu Stadium.
However, Simeone does not feel that his side can challenge for the Liga title this time around due to the might of Real and Barcelona.
"The league will still be between Barca and Real Madrid for several years due to their economic strength. That rules us out," he continued.
"In this type of final, anything is possible, but I do not believe so in the league. They both have to fail and that’s very difficult."
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